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Philosophy and Ideas

Science and Its Limits

D.M. Armstrong

The author of this book (What Science Knows)
is one of the most interesting philosophers at present working in
Australia. He is a Professor of Mathematics at the University of New
South Wales. His book The Science of Conjecture was published in 2001. It considers the notions of evidence and probability before Pascal
gave the first mathematical treatment of probability. It was
immediately recognised as a work of wide and rigorous scholarship that,
one might say, created its own field of investigation. Perhaps
something of its width can be appreciated by the headings for the first
chapter, "The Ancient Law of Proof": Egypt and Mesopotamia, the Talmud,
Roman Law, Proof and Presumption, Indian Law. In later chapters,
selecting at random, the contributions of the Witch inquisitors, the
Greek Sophists, the thinking about insurance, annuities, bets and dice
in the ancient and medieval world, are all passed in review. And there
is depth as well as width.

In 2003 Franklin published a history of philosophy in Australia. A
worthy subject, but perhaps a little dull? Not quite. He summoned up
the shade of Socrates and titled it Corrupting the Youth. It is
easily the liveliest history of philosophy ever written. It is true
that Melburnians complained that it was really little more than a
history of Sydney philosophy, and undoubtedly they had a case. But much
may be forgiven this enjoyable book (especially by Sydneysiders as this
reviewer is).

Now we have from him a fascinating book, What Science Knows.
It is a defence and apology for science (against postmodernists and
more subtle opponents). But it should be noticed that he does not think
that all our rational belief is science-based. He speaks already in his
preface of "the essentially non-scientific character of some of the
topics on which we most desire and need knowledge: consciousness and
ethics". (Naturalists such as myself would, of course, not stop at this
point.)

A feature of the book is the inserted boxes that serve all sorts of
purpose: to follow some interesting historical issues such as the case
of the black swans (complete with a picture of such a swan); to give a
mathematical treatment of some points of the argument, together with
some formulas (optional); quotations from inductive sceptics and
critics of inductive scepticism, including David Stove's wonderfully
witty send-up of Popper, Kuhn, Lakatos and Feyerabend's re-writings of
the sentence "Cook discovered Cook Strait"; a physics student's
T-shirt, and much more. The book has some excellent jokes of its own,
my favourite being the useful dictum, "Concepts that need to be
expressed in German are, in general, dubious."

Franklin begins at the beginning: the low-level
generalisations that must be rational if scientific knowledge is to
have any empirical foundation. "All ravens are black" is a traditional
example. "It's in spring that the wheat comes up" is a further example
that he gives. One can go on indefinitely with knowledge such as this.
If it is not rational to accept such generalisations, the huge edifice
of theoretical science lacks a proper observational foundation.
Franklin favours logical probability, a notion to which he was
introduced by David Stove, the most influential of Franklin's
philosophy teachers. The rather controversial idea is that the evidence
of repeated observation of, say, ravens that are black without any
counter-instances, creates an objective probability (though no
certainty) that unobserved ravens will have the same colour of plumage.
The discussion has to get rather technical. But Franklin also draws
attention to an idea that many philosophers are currently attracted to:
it is inference to the best explanation. (I am strongly
attracted myself.) Applied to the case of the ravens it goes like this.
The observed constant colour of ravens needs explanation. The
best explanation would be that being a raven in some way ensures (or
ensures the probability of) blackness of feather. This argument seems
to me to be like the (idealised) village maiden: simple and good. The
seminal idea that there are laws of nature with universal scope then
rather naturally follows.

Logical probability or inference to the best explanation, or both,
would seem to be hopeful ways of making progress with the
philosophically famous problem of induction, bequeathed to
present-day philosophers by David Hume. Franklin then turns to the
congenial task of criticising the inductive sceptics and those he
labels the Enemies of Science. Hume’s quite complex argument is
criticised for simply assuming that probabilistic arguments cannot have
weight. His sin is "deductivism" (Stove's term), that is, the assuming
that what is needed is some deductive proof that, for example, the sun will rise tomorrow.

At this point Franklin pauses to refute the canard that in the
Middle Ages everybody thought the earth was flat. Aquinas for one, he
points out, knew it was spherical. But, he says, the argument for
Earth's sphericity is fairly difficult to mount. It depends on an
inference to the best explanation for various facts such as the
detailed nature of eclipses. This, by the way, indicates that an
inference to the best explanation (or abduction, as it is sometimes
called) is not always so easy as it is in the case of the simple
generalisations already discussed. It takes ingenuity to think the
explanation up, and the explanation then needs, of course, to be tested
by controlled experiments.

Now for the Enemies of Science. The first four are David Stove's
"four modern irrationalists": Popper, Kuhn, Lakatos and Feyerabend.
Popper, correctly I think, gets off relatively lightly. His stress on
the importance of attempts to falsify theories is accepted by Franklin,
but his deductivism, inherited from Hume, means that Popper cannot
consistently claim rational belief for any scientific theory, something
that he never seems to grasp. Kuhn's notion of paradigm shifts that
he thinks are involved in scientific advances, with the new ruling
paradigm theories incomparable with the displaced theories, begins an
unwholesome drift towards relativism about truth. Lakatos and
Feyerabend are of less importance, I think.

Kuhn, in particular, unwittingly prepared the way for the
intellectual horrors of the postmodernist attack on science. Franklin
takes us through the entirely justified Sokal hoax. The physicist Alan
Sokal wrote a nonsensical article on physics, lacing it with
postmodernist slogans as bait. The article was accepted and published
by a postmodernist journal. There were some lines of genuine poetry in
the works of Ern Malley, but Sokal's "paper" is straight garbage.

Franklin then sets himself to discuss the nature of science. He
draws the all-important distinction between the empirical
(observational) sciences and mathematics (together with logic). The
latter may be called the rational sciences. Quite rightly I think, he
rejects the very influential view of W.V. Quine that the distinction
between the two sorts of discipline is one of degree alone. The mark of
the rational sciences is that here we have proof, something that is largely absent in the empirical sciences. A mathematical theorem that, after carefulchecking,
is pronounced proved, stays proved. (Recently illustrated by the
long-sought proof of Fermat's "Last theorem".) Proof is
epistemologically very secure. It is, says Franklin, "the gold standard
of knowledge". (He brushes aside an attempt by Lakatos to re-introduce
doubt in this sphere.)

This epistemological security is, I think, not the only, or even the
main, reason for the importance of mathematics. The laws of nature have
turned out to be susceptible to mathematical modelling, something that
has been clear since the work of Galileo, Descartes and Newton. I don't
think anybody knows how, or even has a good suggestion, to explain
this. In 1960 the physicist Eugene Wigner published an article with a
much quoted title: "The Unreasonable Effectiveness of Mathematics in
the Natural Sciences". Perhaps we will just have to accept this
effectiveness with "natural piety".

Turning to empirical science, Franklin recognises the claim of physics to be the central
empirical discipline. The equations of contemporary quantum physics,
though probabilistic only, are perhaps more securely reliable under
testing than any physical theory that has so far been proposed. There
is something strange though. Though the predictions are spectacularly
accurate, the interpretation of what they say is a scene of wild
disagreement, with tests that would discriminate between views not at
present available. Speaking as a philosopher, I'm tempted to say that
the metaphysics behind the equations is obscure. What seems to be
lacking is some "inference to an explanation" that is then testable. No
doubt the mathematics behind it will be very difficult.

What is the subject matter of mathematics? It is, says Franklin,
"structure, or pattern". This view seems to be the answer that many
other present philosophers of mathematics give, the word pattern
taken from the philosopher of mathematics Michael Resnik. I'd suggest
that the field of pure mathematics could be usefully circumscribed a
little bit more. Using Gilbert Ryle and Jack Smart's terminology, we
can speak of topic neutral structure or pattern, structure that
abstracts from all empirical material. This doesn't mean, however, that
we have to embrace a Platonic heaven of mathematical objects. A
mathematical structure or pattern that was nowhere to be found in the
space-time world—if such there is—would be a mere possibility that we
don’t have to give any ontological credit to.

It remains true, as Franklin says, that "structure" and "pattern"
are terms that are "vague, general and colourless". He immediately
remedies this by a most useful discussion of the key mathematical
properties of symmetry and ratio that are perfectly abstract, but are imaginatively graspable.

As if this were not enough, as it would be for your ordinary author,
there is much else that is of great value in this book. A clear
discussion explains why thought experiments are useful in physics and
other disciplines. A warning is given that where we have complex
working systems, paradigm cases being the human body and still more our
brains, deep scientific explanations are hard to come by. (Sleep is a
baffling problem, but the studies of cognitive development in babies
are praised for their successes.) New semi-mathematical disciplines are
explained and assessed. Probability is discussed, and it is argued that
the social sciences, while not as powerful as other scientific
disciplines, make a real contribution. There is even a useful
discussion of "actually existing science" with its grants and its
refereeing system.

For those who are Christians, as Franklin is, the topic of evolution
is a little delicate. He says that in this field his discussion is not
comprehensive, nor does he seek to establish conclusions. But, he says:
"The logical complexity of the theory itself makes it hard to establish
the theory definitively." He accepts that there is good evidence for "a
common descent from primitive forms". It is the Darwinian mechanism of
evolution where intelligent dissent can be entertained. Can natural
selection (along with sexual selection that seems to explain such a
phenomenon as the peacock's tail) explain the whole of evolutionary
change? Franklin discusses one of the cases brought up by Michael Behe,
the case of the flagellum, an organism that has evolved a propeller.
This, Behe argues in detail, is something that Darwinian theory cannot
explain. Franklin thinks Behe has quite a strong case.

I had the good fortune some years ago to hear Behe talk, at a
symposium on evolution at the University of Notre Dame. I thought at
the time that Darwinians were lucky to have such an informed and
resourceful critic as Behe. Let the chips fall where they may. I'd
myself look for some naturalistic explanation for the whole process of
evolution, but let us not regard the case as closed.

A glutton for punishment, Franklin takes on the climate change
debate as well. His summing up on the two topics is worth quoting in
full:

In both evolution and climate change,
the majority view of the scientific experts is well ahead. In neither
case is there any known coherent alternative. But the complexities of
the evidence are such that a higher standard of politeness to sceptics
who raise serious problems would be well-advised.

(I have just now been reading Ian Plimer's newly appeared book Heaven + Earth, which seems to show that the case for the global warming hypothesis is very weak indeed.)

I do have one difference with Franklin in connection with
evolutionary theory, and that is his rather dim view of
socio-biological theories. He is no doubt right to say that such
theories are hypotheses, and are difficult to test. But I think what
some have called "just so stories" are interesting and exciting
intellectually. They show the empirical possibility of explanations of
various matters. A case in point is the recently published book by
Denis Dutton, The Art Instinct. Art is a very puzzling
phenomenon to capture the lineaments of, and to explain its origin and
continued relevance. Dutton gives us a Darwinian theory of art that
seems to explain these things in a plausible naturalist manner. It came
as a revelation to me. It is true that it is difficult to see how such
a theory can be tested at present. But that may come in the future. In
the meanwhile it is a suggested "inference to the best explanation"
that a naturalist view of human nature should not be without.

This brings me to the last chapter of this book. Franklin argues
that science has its limits. It cannot explain consciousness and it
cannot explain morality. I will start by conceding that these are very
difficult matters, where dogmatism should not be allowed to dictate the
answer. The mind, and in particular the human mind, is very puzzling
affair. The view I favour is that the mind can be identified with the
working of the brain, and that working is a physical process obeying
the same physical laws as the rest of nature. We are introspectively
aware of our own mind, that much can be conceded to Descartes, who
Franklin appeals to. But we are not directly aware what the mind is. It
is not the sort of direct knowledge that would be likely to be thrown
up in the course of evolution. It does not matter when one is engaged
in practical tasks. But it seems a good scientific hypothesis that the
mind's complexity is a physical complexity, dauntingly complex but
still physical. I'd agree, though, that the so-called secondary
qualities, such as colour, sound, taste and smell, pose a difficult
problem for my position. But they don't seem to be the sort of
phenomena on which we can base a worldview.

In discussing morality Franklin appeals to Hume's view that no ought can be deduced from what is.
This is indeed a clever attempt to turn the tables on the naturalist,
using the great naturalist's great weapon. But is Hume a reliable ally
for Franklin? Can one not say that here Hume is still a deductivist as
he was when he was thinking about induction? Franklin points out that
there is some evidence that humans seem to have a moral sense. One
might hope to link this sense, if it exists, with the conditions of
human flourishing. But why should we be too worried about the fact that
moral principles cannot be deduced from human nature?

Regardless of these metaphysical disputes, here is an apology for
science that is intelligent, informed, yet nuanced and engagingly
presented. It deserves to be widely read.

D.M. Armstrong is Emeritus Professor of Philosophy at the University of Sydney.